We note that the transition probability formula (REF ) shares formal similarity with the moment formulas in the \(q\) -TASEP with various initial conditions, see [1]}, where the parameters \(a_i\)  correspond to the \(a_i\)  in our paper. This is not a coincidence: The duality between the \(q\) -TASEP and \(q\) -TAZRP implies that the moment formula for \(q\) -TASEP satisfies the true evolution equation for \(q\) -TAZRP, as explained in [1]}. In the special case where \(a_i\)  are identical, moment formulas in \(q\) -TASEP are derived from properties of \(q\) -TAZRP in [3]}.
